Performative prediction characterizes environments where predictive models alter the very data distributions they aim to forecast, triggering complex feedback loops. While prior research treats single-agent and multi-agent performativity as distinct phenomena, this paper introduces a unified statistical inference framework that bridges these contexts, treating the former as a special case of the latter. Our contribution is two-fold. First, we put forward the Repeated Risk Minimization (RRM) procedure for estimating the performative stability, and establish a rigorous inferential theory for admitting its asymptotic normality and confirming its asymptotic efficiency. Second, for the performative optimality, we introduce a novel two-step plug-in estimator that integrates the idea of Recalibrated Prediction Powered Inference (RePPI) with Importance Sampling, and further provide formal derivations for the Central Limit Theorems of both the underlying distributional parameters and the plug-in results. The theoretical analysis demonstrates that our estimator achieves the semiparametric efficiency bound and maintains robustness under mild distributional misspecification. This work provides a principled toolkit for reliable estimation and decision-making in dynamic, performative environments.

翻译：表演预测描述了预测模型改变其试图预测的数据分布的环境，从而引发复杂的反馈循环。尽管先前研究将单智能体与多智能体表演性视为不同现象，本文提出了一个统一的统计推断框架，将二者联系起来，并将前者视为后者的特例。我们的贡献包括两个方面。首先，我们提出了用于估计表演稳定性的重复风险最小化（RRM）过程，并建立了严格的推断理论，证明了其渐近正态性并确认了其渐近有效性。其次，针对表演最优性，我们引入了一种新颖的两步插件估计器，该估计器将重新校准的预测驱动推断（RePPI）思想与重要性采样相结合，并进一步为底层分布参数和插件结果的中心极限定理提供了形式化推导。理论分析表明，我们的估计器达到了半参数效率界，并在温和分布设定错误下保持鲁棒性。这项工作为动态表演环境中可靠的估计与决策提供了原则性工具包。